I think my cat would like a Miniture Dachsund to play with

I have a three year old orange tabby called Hank.  Hank is a very sociable cat and he's always bringing over the local neighborhood cats for treats when he thinks that maybe they're not getting enough at home.  He has a lot of feline friends and recently I noticed that he seemed a bit lost when his most recent friend stopped coming by,  I have always toyed with the idea of getting a small dog but worried that because I am such a cat person that I wouldn't really appreciate a dog as much as another cat, but I think that the cat I have now might actually do better with a small dog than another cat. Though Hank likes being friends with the local cats he doesn't really have that buddy buddy thing going that I think he'd like with another animal.  I know I must sound off my rocker but I really think he would do well with a breed like a miniature Dachshund.   What do you think?  Do you think a very social cat would do well with a small dog?